Curved sandwich panels with two aluminium face sheets and an aluminium foam core under air blast loadings were investigated experimentally and numerically. Specimens with two values of radius of curvature and different core/face sheet configurations with the same projected area were tested for three blast intensities. All four edges of the panels were fully clamped. The experiments were carried out by a four-cable ballistic pendulum with corresponding sensors. The impulse acting on the front face of the assembly, the deflection history at the center of the back face sheet, and the strain history at some characteristic points on the back face were obtained. Then the deformation/failure modes of specimens were classified and analyzed systematically. The commercial software LS-DYNA was employed to simulate those physical processes. The finite-element (FE) model was validated by the data from experiments. Detailed deformation and energy dissipation mechanisms were further revealed by the FE models. The valuable experimental data and results from FE models show that the initial curvature of a curved sandwich panel changes the deformation/collapse mode with an extended range for bending-dominated deformation mode, which suggests that the performance of the sandwich shell structures slightly exceeds that of both their equivalent solid counterpart and a flat sandwich plate in certain blast intensity ranges.